Thread Rating:
  • 0 Vote(s) - 0 Average
  • 1
  • 2
  • 3
  • 4
  • 5
Elliptic Superfunctions
#1
From the double-angle formulas for the Jacobi elliptic functions:
, we can get superfunctions to other rational functions.

For example, , if my computations are correct, is the superfunction for:
, or
.

So for example, picking the modulus to be k=-3, we would get: . This means that would be the superfunction for , which is well outside the Mandelbrot set.
Reply
#2
(08/17/2010, 10:39 PM)tommy1729 Wrote: like i said mike , if you read my reply : i think he meant cn instead of nc.

and i pointed out that a periodic function is not a superfunction in the direction of its period.

regards

tommy1729

(Oo, I just deleted that post, I didn't think someone would have gotten to it already... (Just for reference: the post was asking about what "nc" was since I hadn't seen it before, then I looked it up and saw it really does exist and that's why I deleted it))

Yeah, but is not periodic in the real axis direction due to the exponential (it does have an imaginary period of but not a real one) It's not straight , but composed with an exponential.

Reply
#3
(08/17/2010, 05:39 AM)BenStandeven Wrote: From the double-angle formulas for the Jacobi elliptic functions we can get superfunctions to other rational functions.

Actually this topic was already considered in:
Schröder, E. (1871). Ueber iterirte Functionen. (On iterated functions.). Clebsch Ann., 3, 296–322.

Personally interesting for me would be the iterates/superfunctions of rational functions that dont have a real fixed point. Are there some amongst this class obtained from elliptic addition theorems?

In the case of several real fixed points there is still always the question at which fixpoint the obtained elementary iteration/superfunction is the regular iteration/superfunction.
Reply


Possibly Related Threads...
Thread Author Replies Views Last Post
  Superfunctions in continu sum equations tommy1729 0 1,951 01/03/2013, 12:02 AM
Last Post: tommy1729
  superfunctions of eta converge towards each other sheldonison 13 15,509 12/05/2012, 12:22 AM
Last Post: sheldonison
  how many superfunctions? [was superfunctions of eta converge towards each other] tommy1729 8 9,218 05/31/2011, 07:38 PM
Last Post: sheldonison
  elementary superfunctions bo198214 37 35,020 04/25/2010, 05:15 PM
Last Post: bo198214



Users browsing this thread: 1 Guest(s)